Fluid interfaces with very sharp tips in viscous flow

Sylvain Courrech du Pont, Jens G Eggers*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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When a fluid interface is subjected to a strong viscous flow, it tends to develop near-conical ends with pointed tips so sharp, their radius of curvature is undetectable. In microfluidic applications, tips can be made to eject fine jets, from which micron-sized drops can be produced. Here we show theoretically that the opening angle of the conical interface varies on a logarithmic scale as function of the distance from the tip, owing to non-local coupling between the tip and the external flow. Using this insight we are able to show that the tip curvature grows like the exponential of the square of the strength of the external flow, and to calculate the universal shape of the interface near the tip. Our experiments confirm the scaling of the tip curvature as well as of the interface's universal shape. Our analytical technique, based on an integral over the surface, may also have far wider applications, for example treating problems with electric fields, such as electrosprays.
Original languageEnglish
Pages (from-to)32238-32243
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number51
Early online date7 Dec 2020
Publication statusPublished - 22 Dec 2020


  • free surface flows
  • singularities
  • selective withdrawal
  • microfluidics


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